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Noise in Short Channel MOSFETs

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Presentation on theme: "Noise in Short Channel MOSFETs"— Presentation transcript:

1 Noise in Short Channel MOSFETs
John A. McNeill Worcester Polytechnic Institute (WPI), Worcester, MA

2 Overview Creativity in Analog / Mixed Signal IC Design
DSM CMOS Effects on Analog Design Fundamental Noise Sources Applications Conclusion

3 Overview Creativity in Analog / Mixed Signal IC Design
Role of Creativity DSM CMOS Effects on Analog Design Fundamental Noise Sources Applications Conclusion

4 Career Classification
CREATIVE USEFUL ARTIST POET TEACHER NURSE PROFESSOR ENGINEER ADVERTISING DOCTOR INVESTMENT BANKER LAWYER GOOD PAY

5 Why be creative? Need Easy problems solved already
Tough problems need creative solution Dealing with environment of change Coping vs. thriving Human nature Fun!

6 Creativity Resources

7 Creativity Framework Explorer Artist Judge Warrior

8 Example: Time (Stages of project)
Explorer Artist Judge Warrior Background Research Brainstorm Options Choose Solution Implement Design

9 Creativity Framework Explorer Artist Judge Warrior
Seek out new information Survey the landscape Get off the beaten path Poke around in unrelated areas Gather lots of ideas Shift your mindset Don't overlook the obvious Look for unusual patterns

10 Creativity Framework Explorer Artist Judge Warrior
Create something original Multiply options Use your imagination Ask "what if" questions Play with ideas Look for hidden analogies Break the rules Look at things backward Change contexts Play the fool

11 Creativity Framework Explorer Artist Judge Warrior Evaluate options
Ask what's wrong Weigh the risk Embrace failure Question assumptions Look for hidden bias Balance reason and hunches Make a decision!

12 Creativity Framework Explorer Artist Judge Warrior
Put decision into practice Commit to a realistic plan Get help Find your real motivation See difficulty as challenge Avoid excuses Persist through criticism Sell benefits not features Make it happen Learn from every outcome

13 Example: Modes of Thinking
Explorer Artist Judge Warrior Divergent Soft Qualitative Convergent Hard Quantitative

14 Why a Creativity Model? Education Standardized-test-numbed students
Paralysis in face of open-ended problem Designer Awareness of strengths, weaknesses Recognize preferences Not Right or Wrong! One way of looking at process Orchard analogy

15 Creativity Framework Explorer Artist Judge Warrior
Survey the landscape Break the rules Question assumptions Learn from every outcome

16 Overview Creativity in Analog / Mixed Signal IC Design
DSM CMOS Effects on Analog Design Short Channel Effects Noise Behavior Fundamental Noise Sources Applications Conclusion Survey the landscape

17 Good Old Days W/L ID Large strong inversion “square law” region
WEAK INVERSION VELOCITY SATURATION Large strong inversion “square law” region “Easy hand analysis Op 't Eynde and Sansen, "Design and Optimization of CMOS Wideband Amplifiers," CICC 1989

18 TSMC L=0.25µm process W [µm] ID [µA] Square law
104 W [µm] WEAK INVERSION 103 102 101 VELOCITY SATURATION ID [µA] 100 10-6 10-5 10-4 10-3 10-2 Square law Graphical / numerical analysis

19 MOSFET Noise Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.

20 MOSFET Noise p.s.d. Saturation, strong inversion operation
[A2/Hz] 1/f REGION WHITE NOISE REGION Saturation, strong inversion operation Where does factor g=2/3 come from? Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.

21 Submicron CMOS: Noise behavior
Gamma factor g > 2/3 ?!? Disagreement with long channel model? Question assumptions Navid, Lee, and Dutton," A Circuit-Based Noise Parameter Extraction Technique for MOSFETs," ISCAS 2007, pp

22 Overview Creativity in Analog / Mixed Signal IC Design
DSM CMOS Effects on Analog Design Fundamental Noise Sources Shot Noise Thermal Noise Applications Conclusion

23 Shot Noise Current noise density for DC current IDC
Where does this come from? Key assumption: Electron arrivals independent events

24 Shot Noise What is current measured by ammeter?

25 Shot Noise What is current measured by ammeter?

26 Ramo-Shockley Theorem
Current measured by ammeter: Randomly arriving pulses with area qe

27 Poisson Process Average arrival rate  [sec-1] Average DC current:
AUTOCORRELATION Average arrival rate  [sec-1] Average DC current: Autocorrelation: time domain description of random process

28 Shot Noise Power Spectral Density
Wiener-Khinchine theorem Autocorrelation  frequency domain p.s.d Frequency domain For frequencies < 1/T

29 Shot Noise Power Spectral Density
Key Points: Discrete nature of charge is essential Carrier transits are independent events Carriers do not interact with each other or with any medium Temperature not a factor

30 Thermal Noise Current noise density for resistor
Where does this come from? Assumption: Carriers in thermal equilibrium

31 Thermal Noise in Resistor
Assumption: Carriers in thermal equilibrium Random velocity vectors v Only vx component contributes to current

32 "Temperature in this room is 293K"
Boltzmann's Constant k k = 1.38 E-23 J/K Meaning? Thermodynamics: Equipartition theorem Independent energy storage modes in a system at equilibrium have average energy of kT/2 Equivalent statements: "Temperature in this room is 293K" "Average kinetic energy (in each of x, y, z directions) for each air molecule in this room is 2.02E-21 joule"

33 Thermal Noise Approximate collision statistics: Mean free path lc
Mean free time tc 1 ps Velocity (rms) vx 0.1 µm/ps

34 Thermal Noise Consider "slice" equal to mean free path lc
During one mean free time tc On average, half of carriers exit each way: IAVG+ = IAVG- Shot noise components is+ = -is- correlated Noise current from "slice" is = 2is+ Sarpeshkar, Delbruck, and Mead, "White noise in MOS transistors and resistors," IEEE Circuits & Devices Magazine, Nov. 1993

35 Thermal Noise Sum (independent) contributions from slices
Noise current seen by external ammeter im(s) reduced by current divider factor: DR of slice, total resistance R = R1 + DR + R2 Relating to R using mobility definition gives Sarpeshkar, Delbruck, and Mead, "White noise in MOS transistors and resistors," IEEE Circuits & Devices Magazine, Nov. 1993

36 Thermal Noise (Alternative)
Equipartition, rms energy in capacitor: Integrate noise p.s.d. over noise bandwidth: Equate:

37 Thermal Noise Power Spectral Density
Key Points: Discrete nature of charge is not essential Can also be derived from equipartition only (e.g. kT/C noise) Carrier scattering: interact with medium, thermal equilibrium Carrier transits are not independent due to interaction with medium Temperature is important to determine carrier average kinetic energy / velocity

38 Overview Creativity in Analog / Mixed Signal IC Design
DSM CMOS Effects on Analog Design Fundamental Noise Sources Application MOSFET Noise Oscillator Jitter Conclusion

39 MOSFET Channel Noise Density
Where does this come from? Assumption: Resistive channel segments Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.

40 MOSFET Noise Analysis NOISE DRAIN SOURCE Model: Thermal noise dv for differential segment dx of MOSFET channel Integrate over channel length L Gamma factor g = 2/3 falls out of integral A. Jordan and N. Jordan, "Theory of noise in MOS devices," IEEE Trans. Electron Devices, March, 1965

41 MOSFET Noise Analysis Key assumption:
Carrier behavior in channel determined by mobility (resistive) behavior What if it's not a resistor? Ask "what if" questions

42 Velocity Saturation Deviation from mobility model at high field
"High field"  Small dimensions Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, 2008.

43 MOSFET Potential Energy (L ~ µm)
Carrier injection into channel Low field motion modeled by mobility Velocity saturated region

44 MOSFET Potential Energy (L < µm)
Velocity saturated region is a greater fraction of channel Carriers still interact due to collisions

45 MOSFET Potential Energy (L << µm)
Channel length L ~ mean free path lc "Ballistic": no interaction due to collisions No thermal equilibrium

46 L < lc "Breaking the Rules"
L < mean free path lc No thermal equilibrium No reason to expect any validity for a thermal noise / resistance model that assumed mobility and thermal equilibrium Behavior dominated by statistics of carrier injection at source Shot noise! But not full shot noise: Presence of injected carrier modifies potential profile; changes probability of injection

47 Analogy: Bipolar Transistor
Output current noise ino for isolated bipolar transistor is full shot noise inc of collector current With degeneration resistor: Not full shot noise: Voltage drop across RE modifies vBE ; feedback reduces variation in ino due to inc

48 Submicron CMOS: Noise behavior
Shot noise prediction Don't interpret as g increase Interpret as shot noise suppression Navid, Lee, and Dutton," A Circuit-Based Noise Parameter Extraction Technique for MOSFETs," ISCAS 2007, pp

49 Overview Creativity in Analog / Mixed Signal IC Design
DSM CMOS Effects on Analog Design Fundamental Noise Sources Application MOSFET Noise Oscillator Jitter Conclusion

50 Jitter Example: Ring Oscillator
Time-domain noise (jitter) on clock transitions Characterized by standard deviation  (ps rms)

51 Jitter Example: Ring Oscillator
Plot jitter vs. time interval ∆T Increases as square root: jitter delay  frequency-independent figure-of-merit McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009

52 Jitter at the Gate Delay Level
MOSFET noise adds uncertainty to gate delay Td Statistics of MOSFET noise can be related to oscillator figure-of-merit  McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009

53 How to Improve Jitter? Burn more power
Oscillator figure-of-merit  of form Derived from thermal noise model Intuitively, as oscillator power increases, random thermal energy is a smaller fraction of waveform McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009

54 Oscillator Jitter  vs. W
Scales as predicted Chengxin Liu, "Jitter in Oscillators …," PhD Dissertation, WPI, 2006

55 How to Improve Jitter? Burn more power
Oscillator figure-of-merit  of form Derived from thermal noise model How does this behave as L shrinks? McNeill and Ricketts, "The Designer's Guide to Jitter in Ring Oscillators," Springer, 2009

56 Oscillator Jitter  vs. L
? ? Deviation from predicted for L < 1µm Inflection or minimum? Chengxin Liu, "Jitter in Oscillators …," PhD Dissertation, WPI, 2006

57 Overview Creativity in Analog / Mixed Signal IC Design
DSM CMOS Effects on Analog Design Fundamental Noise Sources Applications Conclusion Learn from every outcome

58 DSM CMOS Conclusions Survey the landscape
Noise behavior changes for short L Question assumptions Mobility model Ask "what if" questions What if it's not a resistor? Learn from every outcome Jitter example: Scaling may not provide benefits for analog as one might expect from long channel model

59 Design Drivers in DSM CMOS
Environment: Decreasing ability to predict analog performance from simple assumptions / models Explorer Artist Judge Warrior Add Complexity Eliminate Complexity Digital Analog

60 Acknowledgments WPI David Cyganski Chengxin Liu Analog Devices
Mike Coln Bob Adams Larry DeVito Colin Lyden Carnegie Mellon David Ricketts Columbia University Yannis Tsividis Creativity Resources Roger von Oech

61

62 References Creativity MOSFET Device Physics CMOS Design
R. Von Oech, "A Whack on the Side of the Head" New York: Warner, ISBN R. Von Oech, "A Kick in the Seat of the Pants" New York: HarperCollins, ISBN MOSFET Device Physics Y. Tsividis, "Operation and Modeling of the MOS Transistor" New York: Oxford University Press, ISBN CMOS Design Op 't Eynde and Sansen, "Design and Optimization of CMOS Wideband Amplifiers," Proc. CICC, 1989. Oscillator Jitter J. McNeill and D. Ricketts, "The Designer's Guide to Jitter in Ring Oscillators" New York: Springer, ISBN


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